Question

A new cafe opens in a country town. The manager of the cafe decides not to invest in advertising
because the coffee is so good that he is confident that word will spread of the new cafe and its
wonderful coffee. A marketing survey has shown that the percentage of the population in the country
town who will hear of this new cafe is governed by the logistic model:

P(t) = A/B + e^(−kt)

where P(t) represents the percentage of the town’s population who hear about the cafe t days after
the cafe opens. The constants A, B and k are to be determined from observations found by t